Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#11923958 | C3 | semidirect |
| 4. C3×(C43⋊C9)⋊C9 | C3 | semidirect |
| 5. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 6. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 7. #23782722 | C3 | semidirect |
| 8. #23782722 | C3 | semidirect |
| 11. #23782713 | C3 | semidirect |
| 12. #23782713 | C3 | semidirect |
| 13. C9×3−1+2×C43 | C3 | semidirect |
| 20. #16812511 | C9 | semidirect |
| 42. #11923958 | C3×C9 | semidirect |
| 56. C3×C43⋊C9 | C3×C9 | semidirect |
| 60. 3−1+2×C43 | C3×C9 | semidirect |
| 95. C9×3−1+2 | C43⋊C3 | semidirect |
| 139. C43 | #731⋊C9 | semidirect |
| 145. 3−1+2 | C9×C43⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812511 | 3 |
| C9×#11923958 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| 3−1+2⋊(C43⋊C9) | 3 |
| #23782722 | 3 |
| #23782719 | 3 |
| #23782713 | 3 |
| C9×3−1+2×C43 | 3 |
| #731⋊C9 | 43 |